Solving Natural Conic Formulations with Hypatia.jl

Published Online:https://doi.org/10.1287/ijoc.2022.1202

References

  • Agrawal A, Diamond S, Boyd S (2019) Disciplined geometric programming. Optim. Lett. 13(5):961–976.CrossrefGoogle Scholar
  • Andersen M, Dahl J, Liu Z, Vandenberghe L, Sra S, Nowozin S, Wright S (2011) Interior-point methods for large-scale cone programming. Optimization for Machine Learning (The MIT Press, Cambridge, MA), 55–83.Google Scholar
  • Ben-Tal A, Nemirovski A (2001) Lectures on Modern Convex Optimization: Analysis, Algorithms, and Engineering Applications, vol. 2 (SIAM, Philadelphia).CrossrefGoogle Scholar
  • Bezanson J, Edelman A, Karpinski S, Shah VB (2017) Julia: A fresh approach to numerical computing. SIAM Rev. 59(1):65–98.CrossrefGoogle Scholar
  • Borchers B (1999) CSDP, a C library for semidefinite programming. Optim. Methods Software 11(1-4):613–623.CrossrefGoogle Scholar
  • Boyd S, Vandenberghe L (2004) Convex Optimization (Cambridge University Press, Cambridge, UK).CrossrefGoogle Scholar
  • Coey C, Kapelevich L (2021) Hypatia.jl version v2021.0177. http://dx.doi.org/10.5281/zenodo.6466746, available for download from https://github.com/INFORMSJoC/2021.0177.Google Scholar
  • Coey C, Kapelevich L, Vielma JP (2021a) Conic optimization with spectral functions on Euclidean Jordan algebras. Preprint, submitted November 2, https://arxiv.org/abs/2103.04104.Google Scholar
  • Coey C, Kapelevich L, Vielma JP (2021b) Hypatia cones reference. Accessed June 1, 2021, https://github.com/chriscoey/Hypatia.jl/wiki/.Google Scholar
  • Coey C, Kapelevich L, Vielma JP (2021c) Hypatia documentation. Accessed May 19, 2022, https://chriscoey.github.io/Hypatia.jl/dev/.Google Scholar
  • Coey C, Kapelevich L, Vielma JP (2021d) Performance enhancements for a generic conic interior point algorithm. Preprint, submitted July 9, https://arxiv.org/abs/2107.04262.Google Scholar
  • Coey C, Lubin M, Vielma JP (2020) Outer approximation with conic certificates for mixed-integer convex problems. Math. Programming Comput. 12:249–293.CrossrefGoogle Scholar
  • Dahl J, Andersen ED (2021) A primal-dual interior-point algorithm for nonsymmetric exponential-cone optimization. Math. Programming 1–30.Google Scholar
  • Diamond S, Boyd S (2016) CVXPY: A Python-embedded modeling language for convex optimization. J. Machine Learn. Res. 17(1):2909–2913.Google Scholar
  • Domahidi A, Chu E, Boyd S (2013) ECOS: An SOCP solver for embedded systems. Proc. Eur. Control Conf. (IEEE, New York), 3071–3076.Google Scholar
  • Dunning I, Huchette J, Lubin M (2017) JuMP: A modeling language for mathematical optimization. SIAM Rev. 59(2):295–320.CrossrefGoogle Scholar
  • Grant M, Boyd S (2014) CVX: MATLAB software for disciplined convex programming, version 2.1.Google Scholar
  • Güler O (1996) Barrier functions in interior point methods. Math. Oper. Res. 21(4):860–885.LinkGoogle Scholar
  • Gurobi (2022) Documentation: Choosing the right algorithm. https://www.gurobi.com/documentation/9.5/refman/choosing_the_right_algorit.html.Google Scholar
  • Hall G (2019) Engineering and business applications of sum of squares polynomials. Preprint, submitted June 19, https://arxiv.org/abs/1906.07961.Google Scholar
  • Kapelevich L, Coey C, Vielma JP (2021) Sum of squares generalizations for conic sets. Preprint, submitted November 2, https://arxiv.org/abs/2103.11499.Google Scholar
  • Legat B, Dowson O, Garcia JD, Lubin M (2022) MathOptInterface: A data structure for mathematical optimization problems. INFORMS J. Comput. 34(2):672–689.Google Scholar
  • Lubin M, Yamangil E, Bent R, Vielma JP (2016) Extended formulations in mixed-integer convex programming. Louveaux Q, Skutella M, eds. Integer Programming and Combinatorial Optimization: 18th Internat. Conf. (Sprinter International Publishing, Berlin), 102–113.Google Scholar
  • MOSEK ApS (2020a) Modeling cookbook revision 3.2.1. https://docs.mosek.com/modeling-cookbook/index.html.Google Scholar
  • MOSEK ApS (2020b) MOSEK fusion API for Python. https://docs.mosek.com/9.1/pythonfusion/index.html.Google Scholar
  • Nesterov Y (2006) Constructing self-concordant barriers for convex cones. Center for Operations Research and Econometrics (CORE) discussion paper, Catholic University of Louvain (UCL), Louvain-la-Neuve, Belgium.Google Scholar
  • Nesterov Y (2012) Toward non-symmetric conic optimization. Optim. Methods Software 27(4-5):893–917.CrossrefGoogle Scholar
  • Nesterov Y, Nemirovskii A (1994) Interior-Point Polynomial Algorithms in Convex Programming. Studies in Applied Mathematics (Society for Industrial and Applied Mathematics, Philadelphia).CrossrefGoogle Scholar
  • Nesterov YE, Todd MJ (1997) Self-scaled barriers and interior-point methods for convex programming. Math. Oper. Res. 22(1):1–42.LinkGoogle Scholar
  • Nesterov YE, Todd MJ, Ye Y (1996) Infeasible-start primal-dual methods and infeasibility detectors for nonlinear programming problems. Technical report, Cornell University Operations Research and Industrial Engineering, Ithaca, NY.Google Scholar
  • O’Donoghue B, Chu E, Parikh N, Boyd S (2016) Conic optimization via operator splitting and homogeneous self-dual embedding. J. Optim. Theory Appl. 169(3):1042–1068.CrossrefGoogle Scholar
  • Papp D, Alizadeh F (2014) Shape-constrained estimation using nonnegative splines. J. Comput. Graphics Statist. 23(1):211–231.CrossrefGoogle Scholar
  • Papp D, Yildiz S (2017) On “A homogeneous interior-point algorithm for non-symmetric convex conic optimization”. Preprint, submitted June 14, https://arxiv.org/abs/1712.00492.Google Scholar
  • Papp D, Yildiz S (2019) Sum-of-squares optimization without semidefinite programming. SIAM J. Optim. 29(1):822–851.CrossrefGoogle Scholar
  • Papp D, Yildiz S (2022) Alfonso: Matlab package for nonsymmetric conic optimization. INFORMS J. Comput. 34(1):11–19.LinkGoogle Scholar
  • Permenter F, Friberg HA, Andersen ED (2017) Solving conic optimization problems via self-dual embedding and facial reduction: A unified approach. SIAM J. Optim. 27(3):1257–1282.CrossrefGoogle Scholar
  • Recht B, Fazel M, Parrilo PA (2010) Guaranteed minimum-rank solutions of linear matrix equations via nuclear norm minimization. SIAM Rev. 52(3):471–501.CrossrefGoogle Scholar
  • Serrano SA (2015) Algorithms for unsymmetric cone optimization and an implementation for problems with the exponential cone. PhD thesis, Stanford University, Stanford, CA.Google Scholar
  • Skajaa A, Ye Y (2015) A homogeneous interior-point algorithm for nonsymmetric convex conic optimization. Math. Programming 150(2):391–422.CrossrefGoogle Scholar
  • Udell M, Mohan K, Zeng D, Hong J, Diamond S, Boyd S (2014) Convex optimization in Julia. Proc. 1st First Workshop for High Performance Technical Comput. in Dynamic Languages (IEEE, New York), 18–28.Google Scholar
  • Vandenberghe L (2010) The CVXOPT linear and quadratic cone program solvers. https://www.seas.ucla.edu/ vandenbe/publications/coneprog.pdf.Google Scholar
  • Yamashita M, Fujisawa K, Kojima M (2003) Implementation and evaluation of SDPA 6.0 (semidefinite programming algorithm 6.0). Optim. Methods Software 18(4):491–505.CrossrefGoogle Scholar
  • Yang J, Luo L, Qian J, Tai Y, Zhang F, Xu Y (2016) Nuclear norm based matrix regression with applications to face recognition with occlusion and illumination changes. IEEE Trans. Pattern Anal. Machine Intelligence 39(1):156–171.CrossrefGoogle Scholar
INFORMS site uses cookies to store information on your computer. Some are essential to make our site work; Others help us improve the user experience. By using this site, you consent to the placement of these cookies. Please read our Privacy Statement to learn more.